Contemporary Abstract Algebra9th EditionJoseph Gallian Publisher: Cengage LearningISBN: 9781305657960
Contemporary Abstract Algebra
Solutions for Contemporary Abstract Algebra
Problem 1E:
Which of the following binary operations are closed? a. subtraction of positive integers b. division...Problem 2E:
Which of the following binary operations are associative? a. subtraction of integers b. division of...Problem 3E:
Which of the following binary operations are commutative? a. substraction of integers b. division of...Problem 4E:
Which of the following sets are closed under the given operation? a. {0, 4, 8, 12} addition mod 16...Problem 5E:
In each case, find the inverse of the element under the given operation. a. 13 in Z20 b. 13 in U(14)...Problem 6E:
In each case, perform the indicated operation. a. In C*, (7+5i)(3+2i) b. In GL(2,Z13) , det [7415]...Problem 8E:
List the elements of U(20).Problem 9E:
Show that {1, 2, 3} under multiplication modulo 4 is not a group but that {1, 2, 3, 4} under...Problem 10E:
Show that the group GL(2,R) of Example 9 is non-Abelian by exhibitinga pair of matrices A and B in...Problem 11E:
Let a belong to a group and a12=e . Express the inverse of each of the elements a, a6,a8,anda11 in...Problem 12E:
In U(9)find the inverse of 2, 7, and 8.Problem 13E:
Translate each of the following multiplicative expressions into itsadditive counterpart. Assume that...Problem 15E:
Suppose that a and b belong to a group and a5=eandb7=e .Write a2b4and(a2b4)2 without using negative...Problem 16E:
Show that the set {5, 15, 25, 35} is a group under multiplication modulo 40. What is the identity...Problem 18E:
List the members of K=x2xD4andL=xD4x2=e .Problem 19E:
Prove that the set of all 22 matrices with entries from R and determinant +1 is a group under matrix...Problem 20E:
For any integer n2 , show that there are at least two elements inU(n) that satisfy x2=1 .Problem 21E:
An abstract algebra teacher intended to give a typist a list of nine integers that form a group...Problem 22E:
Let G be a group with the property that for any x, y, z in the group, xy=zx implies y=z . Prove that...Problem 23E:
(Law of Exponents for Abelian Groups) Let a and b be elements of an Abelian group and let n be any...Problem 24E:
(SocksShoes Property) Draw an analogy between the statement (ab)1=b1a1 and the act of putting on and...Problem 26E:
Prove that in a group, (a1)1=a for all a.Problem 29E:
The integers 5 and 15 are among a collection of 12 integers that form a group under multiplication...Problem 32E:
Construct a Cayley table for U(12).Problem 34E:
Prove that in a group, (ab)2=a2b2 if and only if ab=ba . Prove that in a group, (ab)2=b2a2 if and...Problem 35E:
Let a, b, and c be elements of a group. Solve the equation axb=c for x. Solve a1xa=c for x.Problem 37E:
Let G be a finite group. Show that the number of elements x of Gsuch that x3=e is odd. Show that the...Problem 38E:
Give an example of a group with elements a, b, c, d, and x such that axb=cxd but abcd . (Hence...Problem 39E:
Suppose that G is a group with the property that for every choice of elements in G, axb=cxd implies...Problem 40E:
Find an element X in D4 such that R90VXH=D .Problem 42E:
Suppose F1andF2 are distinct reflections in a dihedral group Dn such that F1F2=F2F1. Prove that...Problem 43E:
Let R be any fixed rotation and F any fixed reflection in a dihedral group. Prove that RkFRk=F .Problem 44E:
Let R be any fixed rotation and F any fixed reflection in a dihedral group. Prove that FRkF=Rk . Why...Problem 45E:
In the dihedral group Dn , let R=R360/n and let F be any reflection.Write each of the following...Problem 46E:
Prove that the set of all 33 matrices with real entries of the form [ 1 a b 0 1 c 0 0 1] is a group....Problem 47E:
Prove that if G is a group with the property that the square of every element is the identity, then...Problem 48E:
In a finite group, show that the number of nonidentity elements that satisfy the equation x5=e is a...Problem 49E:
List the six elements of GL(2,Z2) . Show that this group is non-Abelian by finding two elements that...Problem 50E:
Prove the assertion made in Example 19 that the set 1,2,...,n1 is a group under multiplication...Browse All Chapters of This Textbook
Chapter 0 - PreliminariesChapter 1 - Introduction To GroupsChapter 2 - GroupsChapter 3 - Finite Groups; SubgroupsChapter 4 - Cyclic GroupsChapter 5 - Permutation GroupsChapter 6 - IsomorphismsChapter 7 - Cosets And Lagrange’s TheoremChapter 9 - Normal Subgroups And Factor GroupsChapter 10 - Group Homomorphisms
Chapter 12 - Introduction To RingsChapter 13 - Integral DomainsChapter 14 - Ideals And Factor RingsChapter 18 - Divisibility In Integral DomainsChapter 20 - Extension FieldsChapter 26 - Generators And RelationsChapter 28 - Frieze Groups And Crystallographic GroupsChapter 30 - Cayley Digraphs Of Groups
Sample Solutions for this Textbook
We offer sample solutions for Contemporary Abstract Algebra homework problems. See examples below:
Chapter 0, Problem 1EGiven: An equilateral triangle. Calculation: Three rotations at 0, 120 and 240 gives the symmetric...Chapter 2, Problem 1EChapter 3, Problem 1EChapter 4, Problem 1EChapter 5, Problem 1EGiven information: Concept used: Isomorphism: - A homomorphism ϕ from G into G¯ is said to be an...Chapter 7, Problem 1EChapter 9, Problem 1E
More Editions of This Book
Corresponding editions of this textbook are also available below:
Contemporary Abstract Algebra.
6th Edition
ISBN: 9780618514717
EBK CONTEMPORARY ABSTRACT ALGEBRA
8th Edition
ISBN: 9780100453074
Contemporary Abstract Algebra
8th Edition
ISBN: 9781133599708
Contemporary Abstract Algebra
8th Edition
ISBN: 9781285402734
Contemporary Abstract Algebra
8th Edition
ISBN: 9788131520741
Student Solutions Manual For Gallian's Contemporary Abstract Algebra, 8th
8th Edition
ISBN: 9781133608530
EBK CONTEMPORARY ABSTRACT ALGEBRA
8th Edition
ISBN: 8220100453076
Contemporary Abstract Algebra, 7th Edition
7th Edition
ISBN: 9780547165097
Student Solutions Manual For Gallian's Contemporary Abstract Algebra, 7th (students Solutions Manual)
7th Edition
ISBN: 9780547165394
Student Solutions Manual for Gallian's Contemporary Abstract Algebra, 9th
9th Edition
ISBN: 9781305657977
Bundle: Contemporary Abstract Algebra, 9th + Student Solutions Manual
9th Edition
ISBN: 9781337501590
EBK CONTEMPORARY ABSTRACT ALGEBRA
9th Edition
ISBN: 8220101434852
EBK CONTEMPORARY ABSTRACT ALGEBRA
9th Edition
ISBN: 9781305887855
Contemporary Abstract Algebra
9th Edition
ISBN: 9781337249560
Contemporary Abstract Algebra
5th Edition
ISBN: 9780618122141
Contemporary Abstract Algebra
10th Edition
ISBN: 9781000337358
CONTEMPORARY ABSTRACT ALGEBRA
10th Edition
ISBN: 9780367651787
Related Algebra Textbooks with Solutions
Still sussing out bartleby
Check out a sample textbook solution.
